• In a small saucepan, warm the milk to around 95-104°F / 35-40°C and pour it into the bowl of a stand mixer. Sprinkle yeast and sugar over the milk. If using active dry yeast, let this sit for around 5-10 minutes until it becomes foamy; if using instant yeast, this step can be skipped.
• Add the flour, salt, and eggs to the milk mixture. Fit the stand mixer with a dough hook attachment. Mix until a thick dough forms.
• Add in the softened butter, a few cubes at a time, and keep mixing on medium speed for around 10 minutes until the sweet roll dough pulls cleanly from the sides of the bowl and it is soft and strong.

Kneading by hand

• Alternatively, knead the dough by hand. Mix the dough with a wooden spoon until it forms a shaggy ball. Pull it onto a floured surface and knead a few cubes at a time in the butter. Knead by hand for around 10 minutes until it becomes an elastic and smooth dough. If you need a break, take it. The dough responds well to resting time.

First Rise

• Once kneaded, form the dough into a dough ball. Transfer the dough to a lightly greased large bowl and cover it with plastic wrap or a damp dish towel.
• Let the dough rise in a warm place until doubled in size, around 1 to 1 ½ hours. The total time will depend on your room temperature. The dough can also be covered tightly and refrigerated for up to 16 hours.

Strawberry Filling

• While the dough rises, make the filling so it has time to chill before using it.
• Roughly chop the strawberries into pieces. Add the strawberries, cornstarch, sugar, lemon juice, and salt to a medium saucepan.
• Let the strawberries heat over low-medium heat until they start to break down. Use a wooden spoon to mash them up a bit as they warm.
• Once they have broken down more and released their juices, turn the heat to medium and let the mixture boil, stirring the whole time. As the mixture boils, it will thicken and become jelly-like. Let it boil for a full 2 minutes, continuously stirring.
• Remove from the heat, scrape into a bowl, and let it cool in the fridge until needed.

Shaping

• Grease or line a 9x13-inch baking dish with parchment paper.
• Punch down the risen dough, then pull it from the bowl onto a lightly floured surface. Dust the top of the dough with some flour.
• If the dough has come from the fridge, it will be very stiff. Let it warm up to room temperature for 10 minutes before rolling.
• Use a rolling pin to roll the dough into a large rectangle measuring around 12x16 inches (30cmx40cm).
• Dollop the cold strawberry mixture over the dough, but keep aside two tablespoons for the frosting.
• An offset spatula spreads the strawberries out, leaving around 2 inches uncovered on the bottom long side. This is because the strawberry mixture gets pushed out a bit when you roll it up, and this helps to stop it from escaping.
• Place the rolls into the prepared pan. Cover the pan and let the rolls rise in a warm spot until doubled in size.

Baking

• Preheat the oven to 350°F /180°C.
• Bake the rolls in the oven for around 25-28 minutes until golden brown. If they are browning too fast, you can cover the top of the rolls loosely with aluminum foil. 

Frosting

• While the rolls are baking, make the frosting. In a large bowl, using a handheld or stand mixer fitted with a whisk or paddle attachment beat the cream cheese and butter together on high speed until smooth and creamy.
• Add the confectioners' sugar, vanilla, reserved strawberry jam, and salt. Beat on low speed to incorporate the sugar, then switch to high and beat until creamy.
• Let the baked buns cool for 20 minutes, then spread on the frosting.